The lateral diffusion of membrane components, and the prevention of lateral diffusion, are both essential to cellular function. Many physiological processes in cell membranes require lateral diffusion: mobile redox carriers in mitochondria, diffusion-coupled activation of transducin by rhodopsin in rod outer segments, aggregation mobile receptors for hormones and antibodies, for example. The diffusion of mobile species may be hindered by the presence of immobile species. This project will use percolation theory and Monte Carlo calculations of diffusion on lattices to analyze the effect of these obstacles on diffusion rates. The process of aggregation, and the effect of aggregates on the diffusion of other species, will be examined. The effect of lipid domains on diffusion will be studied, and the effect of obstacles on mobile redox carriers will be modeled. In many types of cells, the prevention of lateral diffusion in the plasma membrane is essential to cell differentiation. One means of accomplishing this is the membrane skeleton; the spectrin network attached to the erythrocyte plasma membrane is the best known example. Similar networks are found in many other types of cells, such as epithelial and nerve cells. The membrane skeleton obstructs lateral diffusion and provides mechanical reinforcement to the plasma membrane. This project will develop a unified model of these effects, again by means of percolation theory and Monte Carlo calculations. The model will show how the completeness of the spectrin network affects the diffusion coefficient of membrane proteins, and the elasticity and mechanical stability of the membrane skeleton. The results can be used to model the effects of missing or defective spectrin, as in hereditary hemolytic anemia, and to model the changes in diffusion and elasticity as the membrane skeleton is assembled during cell development.